Investigation of scarid data
Molly Wilson
Dec. 2018
Notes 11/11: * figure out dcast issues * replacing NA/0s within pipe
1 Data overview:
- Fish follows (2 min) conducted at sites in Antigua (6), Barbuda (3) and Bonaire (4) from March-August 2017
- Follows tracked time spent grazing, bite rates, and competitive interactions (among scarids and with damselfish)
- Follows targeted Sparisoma viride, Scarus vetula, and Sparisoma aurofrenatum of both initial and terminal phases
- Sparisoma aurofrenatum were not followed in Bonaire, but added in Antigua and Bonaire due to low abundances of other two species. Some sites in Antigua and Barbuda had no/low represenation from terminal phase viride and vetula
- Most eventual analyses will likely focus exclusively on initial phase (standardized size window) S. viride and S. vetula
- site level factors (benthic, fish, and rugosity) assessed at each of the 13 sites
Need to determine appropriate size range for comparison. Because they are not evenly distributed (i.e. larger fish in Bonaire, smaller in Barbuda), I will likely want to compare length-feeding relationships as opposed to pooled averages
2 Examing variable distributions and relationships
2.1 Predictor variables
Potential predictor variables are site-level fish, benthic, and rugosity values. These are likely correlated to one another, and I need to determine which ones I ultimately want to use (if modeling behavioral responses via any multivariate regressions). I can also move to SEM if I want to keep multiple correlated predictors.
First, check distribution of predictor variables of interest: not very normally distributed… 
Variable selection notes: - excluding both carnivore variables as they are highly correlated with scarid biomass and total biomass, eventually I could make these more nuanced by distinguishing actual predators, but right now I don’t think it reflects actual predator populations of >15cm parrotfish - rugosity is highly correlated with turf cover, and scarid density - scarid density: removing for now, because I think it was a bit skewed from Barbuda juveniles - could eventually use consp. scarid length as another indicator of overfishing?
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 1.694 1.5167 0.66913 0.50517 0.30585 0.18692
## Proportion of Variance 0.478 0.3834 0.07462 0.04253 0.01559 0.00582
## Cumulative Proportion 0.478 0.8614 0.93605 0.97859 0.99418 1.00000
2.2 Response variables
Fish-level grazing behaviors (as well as competitive interaction frequency)
2.2.1 Distributions
Variable selection notes: - for_bites is correlated with fr and for_dur, but I will play around with keeping it for now.
3 Grazing boxplots
## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 19329868 9664934 24.48 5.08e-09 ***
## Residuals 80 31586112 394826
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = fr ~ island, data = vet)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -936.8111 -1387.7231 -485.8992 0.0000115
## Barbuda-Bonaire -1058.3667 -1486.4053 -630.3282 0.0000002
## Barbuda-Antigua -121.5556 -670.7081 427.5968 0.8575559
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.731 0.4846
## 80## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 3522230 1761115 26.9 5.52e-10 ***
## Residuals 95 6218718 65460
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = fr ~ island, data = vir, white.adjust = T)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -408.89527 -550.1969 -267.59360 0.0000000
## Barbuda-Bonaire -70.05115 -234.5194 94.41711 0.5698132
## Barbuda-Antigua 338.84411 180.1422 497.54604 0.0000055
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.9125 0.405
## 95
## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 1.582 0.7911 22.98 1.3e-08 ***
## Residuals 80 2.753 0.0344
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = g_frac ~ island, data = vet, white.adjust = T)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -0.27575852 -0.4088858 -0.1426312 0.0000122
## Barbuda-Bonaire -0.29697818 -0.4233524 -0.1706040 0.0000008
## Barbuda-Antigua -0.02121967 -0.1833515 0.1409122 0.9476109
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.1837 0.8325
## 80## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 2.808 1.4040 26.13 9.1e-10 ***
## Residuals 95 5.105 0.0537
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = g_frac ~ island, data = vir, white.adjust = T)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -0.36517814 -0.4932046 -0.23715172 0.0000000
## Barbuda-Bonaire -0.06284811 -0.2118646 0.08616841 0.5760464
## Barbuda-Antigua 0.30233003 0.1585381 0.44612197 0.0000076
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.7501 0.4751
## 95
## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 0.314 0.1571 1.448 0.241
## Residuals 80 8.676 0.1085## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = br ~ island, data = vet)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -0.123227748 -0.3595491 0.11309360 0.4303229
## Barbuda-Bonaire -0.132053164 -0.3563867 0.09228034 0.3427971
## Barbuda-Antigua -0.008825416 -0.2966343 0.27898343 0.9970480
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 10.408 9.601e-05 ***
## 80
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 0.045 0.02253 0.502 0.607
## Residuals 95 4.267 0.04491## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = br ~ island, data = vir, white.adjust = T)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire 0.045754540 -0.07128921 0.1627983 0.6222646
## Barbuda-Bonaire 0.043704156 -0.09252906 0.1799374 0.7260125
## Barbuda-Antigua -0.002050384 -0.13350720 0.1294064 0.9992399
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 10.63 6.823e-05 ***
## 95
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 1457 728.5 7.298 0.00126 **
## Residuals 76 7586 99.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 4 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = for_bites ~ island, data = vet)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -9.09956631 -16.491319 -1.707813 0.0118676
## Barbuda-Bonaire -9.17905349 -16.570807 -1.787300 0.0110379
## Barbuda-Antigua -0.07948718 -9.447089 9.288114 0.9997732
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 2.1906 0.1189
## 76## Df Sum Sq Mean Sq F value Pr(>F)
## island 2 903.1 451.5 13.19 9.77e-06 ***
## Residuals 88 3012.5 34.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 7 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = for_bites ~ island, data = vir, white.adjust = T)
##
## $island
## diff lwr upr p adj
## Antigua-Bonaire -7.291484 -10.6759972 -3.90697129 0.0000050
## Barbuda-Bonaire -3.692020 -7.4808559 0.09681671 0.0578051
## Barbuda-Antigua 3.599465 -0.1446468 7.34357613 0.0621841
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 5.0607 0.00831 **
## 88
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14 Exploratory bivariate plots
4.1 Grazing as a function of fish length
Note: remove G1 grazing instances here?
4.2 Grazing as a function of site traits
Notes: - scarid biomass is not the best predictor once I account for differences between my samples in terms of the sizes of fish I was sampling. I think the grazing/length relationships are much stronger.
- restraining sample size to length windows lowers sample size and makes trends much less pronounced - esp. for phase differences
- reducing sample to individual phase only also blurs trends
4.3 Competitive interactions
5 Model trials
- site-level predictors: scar_bm,scar_den,carn_bm,benthic (pc1,pc2)
- fish-level predictors: species, phase, length
- eventually run separately for different species
- species*scar_bm interaction?
- random effects: island
- response variables: g_frac, br (?), and fr (run separately)
5.1 Mixed effects models
- random effect: island
## Linear mixed-effects model fit by REML
## Data: filter(sum_id_pca1, species_code != "rbp")
## AIC BIC logLik
## 9322.943 9358.316 -4653.471
##
## Random effects:
## Formula: ~1 | island
## (Intercept) Residual
## StdDev: 442.1831 450.4068
##
## Fixed effects: fr ~ phase + length_cm + species + pc1 + pc2
## Value Std.Error DF t-value p-value
## (Intercept) 1326.6141 270.99370 613 4.895369 0.0000
## phaset -163.0290 50.24074 613 -3.244957 0.0012
## length_cm -9.1235 3.52618 613 -2.587367 0.0099
## speciesSparisoma viride -623.1907 37.04353 613 -16.823201 0.0000
## pc1 89.0698 44.32152 613 2.009628 0.0449
## pc2 8.7783 31.20623 613 0.281299 0.7786
## Correlation:
## (Intr) phaset lngth_ spcsSv pc1
## phaset 0.168
## length_cm -0.307 -0.651
## speciesSparisoma viride -0.105 -0.067 0.085
## pc1 0.037 0.050 0.021 0.008
## pc2 0.046 0.007 -0.012 0.003 0.114
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.89990834 -0.56004163 -0.01254647 0.53166747 5.13083127
##
## Number of Observations: 621
## Number of Groups: 3## phase length_cm species pc1 pc2
## 1.749662 1.751095 1.007674 1.021045 1.0134115.2 GAM + GAMM
##
## Family: gaussian
## Link function: identity
##
## Formula:
## fr ~ species + phase + s(length_cm) + s(scar_bm) + s(pc1) + s(pc2)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1088.72 27.46 39.652 < 2e-16 ***
## speciesSparisoma aurofrenatum -508.69 50.10 -10.153 < 2e-16 ***
## speciesSparisoma viride -618.17 33.37 -18.526 < 2e-16 ***
## phaset -111.30 39.36 -2.828 0.00481 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(length_cm) 1.000 1.000 16.207 6.22e-05 ***
## s(scar_bm) 1.006 1.009 2.544 0.11121
## s(pc1) 3.481 4.039 33.161 < 2e-16 ***
## s(pc2) 3.814 4.375 3.524 0.00476 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.513 Deviance explained = 52.1%
## -REML = 5772.3 Scale est. = 1.627e+05 n = 782
5.3 ```
To Do as of Nov. 7
* boosted regression trees ecosphere 2017 adrians paper
* species as random effect